Begin by cutting the new potatoes in half to ensure they cook evenly. Place them in a large pot, adding enough salted water to cover. Bring the water to a boil over high heat and let the potatoes cook for 20 to 25 minutes, until tender but firm.

While the potatoes are boiling, prepare the pesto. In a food processor, combine the fresh basil, toasted pine nuts, nutritional yeast, lemon juice, garlic, and salt. Pulse until finely chopped, then drizzle in olive oil while blending until smooth.

Once the potatoes are cooked, drain them and rinse under cold water to stop cooking. Let them cool briefly until manageable.

In a large mixing bowl, combine the cooled potatoes, pesto, and vegan mayonnaise. Add lemon zest and season with black pepper. Toss gently until all potatoes are coated.

Sprinkle remaining toasted pine nuts on top and garnish with extra chopped basil if desired. Serve immediately or refrigerate for up to 4 days.